Of
Snowflakes,
Ice, Figure Skating,
and a Very Brief Bit
About Hexaflexagons

February
12, 2006 was the biggest snowfall in New Yorks history: about
26.9 inches fell in the New York City area. While most of us either
cursed the snow and got out our shovels, or excitedly made forts
and threw snowballs, my attention was taken not by snow en masse
but snow in its most basic component, the snowflake.

Just watching
out the window, I could tell that these snowflakes were going to
be spectacular. I grabbed a square of black velvet from a jewelry
box and headed out, where I investigated the snowflakes that landed
on my square. This was a veritable bonanzain addition to the
usual stellar dendrites, I found radiating stellar dendrites, fernlike
stellar dendrites, and hexagonal crystals.

Simple prism

Hexagonal crystal

Stellar plate

Stellar dendrite

Anyone who wants
to know more about snowflakes should pick up a copy of Kenneth G.
Libbrechts beautiful and informative book, The
Snowflake: Winter's Secret Beauty and go to his site, snowcrystals.com.
Libbrecht, professor of physics and chairman of the physics department
at the California Institute of Technology covers the physics of snow,
the different types of snowflakes, the joys of snowflake watching
and how to photograph snow crystals. He also kindly gave permission
to use these amazing photos of snowflakes from his site, much appreciated
since my own attempts to photograph snowflakes came to naught.

As you notice, many snowflakes
are six-pointed. Thats because H2O molecules line up in a
hexagonal pattern.

According to
Libbrecht, Each red ball represents an oxygen atom, and the
grey sticks represent hydrogen atoms. There are two hydrogens for
each oxygen, making the usual H2O. This, dare I say, makes
snowflakes similar to hexaflexagons;
indeed, if you are at a loss for a design for a hexaflexagon side,
a snowflake always works beautifully.

The
snow crystals grow by faceting and branching, processes that depend
on temperature and humidity. Two common forms of the snow crystal
are the hexagonal prism, in which certain surfaces of the crystal
grow more slowly, and the stellar dendrite, the all-too-familiar branching
structure that is the epitome of what most of us consider snowflake
design. Stellar dendrites are found under higher humidity. When a
bump forms on the surface, water molecules reach the bump before the
rest of the crystal, meaning the bump grows faster. This instability
causes the snow crystals to take on this beautiful form.

Radiating stellar dendrite

Fernlike stellar dendrite

Not all forms
of ice have a hexagonal structure. In addition to ice as we know it,
which scientists call Ice Ih, theres Ice Ic, which are ice crystals
high up in the atmosphere that form cubic crystals. At even higher
pressures, the structure is more compact and dense and no longer hexagonal.
Scientists have created Ice II through XI in the laboratory, including
Ice IX, which forms a tetragonal crystal lattice and is not to be
confused with Ice-9, the doomsday device devised by Kurt Vonnegut
in Cats Cradle. Scientists think that some of these icy variations
could exist in the outer reaches of the solar system.

While on the
subject of ice, I must detour to figure skaters at the Winter Olympics.
With the fairerbut
duller scoring system in place, the skaters seemed to be competing
mostly for the honor of who had the most hideous costume. In my
opinion, the gold medal was won by the mens silver medalist,
who skated to Vivaldis Four Seasons in what looked like different
colored zebra stripes on front and back and long blue sleeves. What
on earth was he thinking?

Best costume
and interpretation had to go to Italian Carolina Kostner who skated,
coincidentally, to Vivaldi and representeda snowflake!

Anyway, lets
leave the cold depths of outer space and Torinos ice rinks
and backtrack back to my snowflake gazing in my own backyard.

I could have
stood for hours staring at these tiny treasures, each so ephemeral.
Staring at snowflakes started to take over my mindit was as
if I could no longer see snow as a huge entity, something for snowplows
to scoop away like so much detritus.

Weve
certainly heard the analogy of snowflakes being compared to people.
Like us, snowflakes vary, each is worthy of inspection and appreciation.
Gathered in large groups (crowds, countries, PTAs, snowforts, avalanches)
we both become something greater and simultaneously lesser.